A semiparametric mixture method for local false discovery rate estimation from multiple studies

Abstract

Antineutrophil cytoplasmic antibody associated vasculitis (AAV) is extremely heterogeneous in clinical presentation and involves multiple organ systems. While the clinical presentation of AAV is diverse, we hypothesized that all AAV share common pathways and tested the hypothesis based on three different microarray studies of peripheral leukocytes, sinus and orbital inflammation disease. For the hypothesis testing we developed a two-component semiparametric mixture model to estimate the local false discovery rates from the $p$-values of three studies. The two pillars of the proposed approach are Efron’s empirical null principle and log-concave density estimation for the alternative distribution. Our method outperforms other existing methods, in particular when the proportion of null is not that high. It is robust against the misspecification of alternative distribution. A unique feature of our method is that it can be extended to compute the local false discovery rates by combining multiple lists of $p$-values.